Impurity radiation corrections

[jonmaddock]

Demonstrates the effect of various options for impurity radiation and allows their plotting: this is not intended to be merged in its current form, but as an investigation. Primarily, this demonstrates the importance of separating the reduced core radiation used for the confinement time calculation and the total radiation considered in the plasma power balance, which I currently believe is incorrect.

I hope the following figures highlight a few things and justify the actual changes I want to make. They are all made with the DEMO LAR solution point and varying tungsten fractions. Deliberate horizontal "jitter" is applied to the scatter plots to ensure overlapping points are discernable.

Impurity radiation profiles

The current impurity power densities are incorrect because they are multiplied prematurely by the normalised minor radius $\rho$ in preparation for the power integral. This has the effect of the power density dropping to 0 for $\rho = 0$, which is incorrect. The core radiation reduction is also evident outside of the confinement time scaling calculation, where it is only intended to be used. This is corrected. The edge integral is now performed explicitly in the 4th subfigure, which is used later subsequently.

Radiation power

When the core radiation reduction is removed, the core radiation obviously increases, but the edge radiation decreases, due to the "edge = total - core" calculation that is currently used. The edge is optionally now integrated explicitly. The total radiation is the same in all cases.

Separate radiation reduction for confinement time scaling only

Two plasma core radiation power densities are now calculated: one for the confinement time scaling only, the other for the rest of the code. They only differ when the `tau E rad reduction` option is selected (brown), which is the only difference between the plots. This separates the radiation calculated for the rest of the models from the reduced value required by the scaling.

Effect on plasma power balance (PPB)

The effect of these various options on the absolute plasma power balance constraint residual in MW (i.e. MW m^-3, then multiplied by plasma volume ) is shown. The "original" point being slightly above zero is probably due to using a slightly out-of-date solution vector relative to the current Process version. One real difference occurs from using the edge radiation in the PPB (purple) which should always be done in my view: the plasma is not in thermal equilibrium if the edge radiation is ignored. The second, larger, difference is due to the use of the reduced core radiation in the confinement time calculation only, rather than globally (i.e. in the PPB too). This is how this "correction" was originally intended to be used I believe: as a way of effectively changing the confinement time scaling for highly-radiative regimes. It should not affect the actual calculated radiation elsewhere in the models. Around 30 MW for low tungsten values is fairly significant.

I would like to always use the un-reduced total radiation (core and edge) in the plasma power balance calculation, and the reduced core radiation in the confinement time calculation only. This would mean that i_rad_loss and f_p_plasma_core_rad_reduction would only apply to the the confinement time calculation. I'm keen to hear your thoughts.

[jonmaddock]

This appears to independently resolve #3968 (comment).

[mkovari]

this is not intended to be merged in its current form, but as an investigation.

Can you clarify this?

[je-cook]

this is not intended to be merged in its current form, but as an investigation.

Can you clarify this?

I think he means it should probably be split into a few separate PRs after the initial review discussion. Also I guess the switches wont be needed if we agree on the solution

[mkovari]

This appears to independently resolve #3968 (comment).

This link is to the comment on volume-integration. Was that intended?

[mkovari]

I think he means it should probably be split into a few separate PRs after the initial review discussion. Also I guess the switches wont be needed if we agree on the solution

So do we actually need to approve the PR?

[je-cook]

no but a review is needed of the content

[grmtrkngtn]

Impurity radiation profiles

I agree with the proposed changes to the impurity radiation profiles. Moving the (\rho) weighting from the stored power-density profile into the volume integral is a clear-cut fix.

Core radiation reduction

I also agree with separating the physical core radiation from the reduced value used in the confinement-time calculation. Retaining the option to apply the reduction to the scaling law only seems like a reasonable compromise but the physical power balance must use the full radiation.

Outstanding

The corrected confinement calculation still relies on two input assumptions: radius_plasma_core_norm and
f_p_plasma_core_rad_reduction.

I'm not sure we still still need the latter, why would we ever not subtract the full radiation (why would we use the factor?)

EUROfusion colleagues have also suggested that the effective core boundary could be calculated from the radial power flow rather than prescribed as an input. My understanding is that METIS calculates the cumulative net power, heating minus local radiation, as a function of radius and uses its maximum to determine the effective transport-driving power. Should we investigate this here, or would that be better treated as a separate follow-up to this accounting PR?